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| Vector Quantization Landmark Points for Supervised Isometric Mapping with Explicit Mapping |
| CHEN Shi-Wen, WANG Xian-Bao, LI Meng-Yuan, YAO Ming-Hai |
| College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023 |
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Abstract Since isometric mapping (ISOMAP) has no supervision and explicit mapping function and other limitations, an improved algorithm, selection of vector quantization landmark points for supervised isometric mapping with explicit mapping (SE-VQ-ISOMAP), is put forward. Firstly, the category information is introduced in the construction of neighborhood graph and geodesic distance matrix. Aiming at the problem that the landmark points are introduced into iterative optimization when distance matrix is processed, a method of vector quantization is employed instead of the traditional random selection. Thus, the whole manifold structure is indicated better by the selected samples. Finally, the radial function is regarded as basis, and consequently explicit mapping of dimensionality reduction method is obtained. On the handwritten digits sets and UCI datasets, the experimental results show that the proposed algorithm is fast and stable with a higher recognition rate.
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Received: 22 July 2014
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[1] Martinez A M, Kak A C. PCA versus LDA. IEEE Trans on Pattern Analysis and Machine Intelligence, 2001, 23(2): 228-233
[2] Cox T F, Cox M A A. Multidimensional Scaling. London, UK: Chapman& Hall, 1994
[3] Tenenbaum J B, de Silva V, Langford J C. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 2000, 290(5500): 2319-2323
[4] Roweis S T, Saul L K. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science, 2000, 290(5500): 2323-2326
[5] Belkin M, Niyogi P. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation, 2003, 15(6): 1373-1396
[6] Zhang Z Y, Zha H Y. Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment. Journal of Shanghai University: English Edition, 2004, 8(4): 406-424
[7] Wu W T. The Application of Manifold Learning Algorithms in Pattern Recognition. Master Dissertation. Shanghai, China: Shanghai Jiao Tong University, 2013 (in Chinese)
(吴文通.流形学习方法在模式识别中的应用研究.硕士学位论文.上海:上海交通大学, 2013)
[8] Geng X, Zhan D C, Zhou Z H. Supervised Nonlinear Dimensionality Reduction for Visualization and Classification. IEEE Trans on Systems, Man, and Cybernetics: Cybernetics, 2005, 35(6): 1098-1107
[9] Li Y. Building K-Edge-Connected Neighborhood Graph for Distance-Based Data Projection. Pattern Recognition Letters, 2005, 26(13): 2015-2021
[10] Zhang Z, Chow T W S, Zhao M B. M-Isomap: Orthogonal Constrained Marginal Isomap for Nonlinear Dimensionality Reduction. IEEE Trans on Cybernetics, 2013, 43(1): 180-191
[11] Sun W W, Halevy A, Benedetto J J, et al. UL-Isomap Based Nonlinear Dimensionality Reduction for Hyperspectral Imagery Classification. ISPRS Journal of Photogrammetry and Remote Sensing, 2014, 89: 25-36
[12] Vlachos M, Domeniconi C, Gunopulos D, et al. Non-linear Dimensionality Reduction Techniques for Classification and Visualization // Proc of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Edmonton, Canada, 2002: 645-651
[13] Wei B L. Video Analysis Using Semi-supervised Manifold Lear-ning. Master Dissertation. Xi′an, China: Xidian University, 2011 (in Chinese)
(魏博兰.半监督流形学习算法在视频分析中的应用.硕士学位论文.西安:西安电子科技大学, 2011)
[14] Cheng Q C,Wang H Y,Feng Y. A Multi-class Multi-manifold Learning Algorithm Based on ISOMAP // Proc of the Chinese Conference on Pattern Recognition. Nanjing, China, 2009. DOI: 10.1109/CCPR.2009.5343987
[15] Wu Y M, Chan K L. An Extended Isomap Algorithm for Learning Multi-class Manidold // Proc of the International Conference on Machine Learning and Cybernetics. Shanghai, China, 2004, VI: 3429-3433
[16] Cho M,Park H. Nonlinear Dimension Reduction Using ISOMap Based on Class Information // Proc of the International Joint Conference on Neural Networks. Atlanta, USA, 2009: 566-570
[17] de Silva V. Tenenbaum J B. Global versus Local Methods in Nonlinear Dimensionality Reduction [EB/OL].[2014-06-30].http://web.mit.edu/cocosci/Papers/nips 02-localglobal-in-press.pdf
[18] Webb A R. Multidimensional Scaling by Iterative Majorization Using Radial Basis Functions. Pattern Recognition, 1995, 28(5): 753-759
[19] Zhang J P, Li S Z, Wang J. Manifold Learning and Applications in Recognition // Tan Y P, Yap K H, Wang L P, eds. Intelligent Multimedia Processing with Soft Computing. Berlin, Germany: Springer-Verlag, 2004: 281-300 |
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2015, Vol. 28 
